Pith Number

pith:7NXDADRN

pith:2010:7NXDADRNC74OOA3IDBDBKJNNF2

not attested not anchored not stored refs pending

The 2d-Directed Spanning Forest is almost surely a tree

CMAP), David Coupier (LPP), Viet Chi Tran (LPP

arxiv:1010.0773 v3 · 2010-10-05 · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7NXDADRNC74OOA3IDBDBKJNNF2}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T03:40:03.609079Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fb6e300e2d17f8e7036818461525ad2e98bf9a4d704e70a78319e28a1a72b0bb

Aliases

arxiv: 1010.0773 · arxiv_version: 1010.0773v3 · doi: 10.48550/arxiv.1010.0773 · pith_short_12: 7NXDADRNC74O · pith_short_16: 7NXDADRNC74OOA3I · pith_short_8: 7NXDADRN

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/7NXDADRNC74OOA3IDBDBKJNNF2 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: fb6e300e2d17f8e7036818461525ad2e98bf9a4d704e70a78319e28a1a72b0bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "79a8859ac533e5b3b3825d13aa131f6d8a855e754281262e7c77468f509d190c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-10-05T06:04:14Z",
    "title_canon_sha256": "59f35c9999e0a3203dddac3ea7c26b5affff976e3bcb74c33c184b9f7cc79c0a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.0773",
    "kind": "arxiv",
    "version": 3
  }
}